I gave this some more thought, and I think you're wrong. Wrong in the sense that Chomsky and Herman did focus on these things. One of the five filters is "Flack". In this filter "wrong" opinions are given flack from institutions with power. The focus on government comes from them being, arguably, the most powerful institution.

The propaganda model does account for other non-governmental and non-media influences. This is talked about in the animation Al-Jazeera made.

https://youtu.be/34LGPIXvU5M